An Introduction to Random Sets

In many fields of probability theory and mathematical statistics, there are several books on similar topics. The theory of random sets is presented much less, partly because it is young, partly because of its complexity. The book by Hung Nguyen demonstrates the variety of tools necessary for development in this field. It begins with some motivating examples of well known random sets in statistics. Then finite random sets are discussed (which are technically easier). When applied in decision making or when studying set valued functions by means of incidence algebras, the beauty of the topic is clearly visible. General random closed set theory starts classically with hit-or-miss topology, the capacity functional and the Choquet theorem. Then a solid background to the Choquet integral (with respect to nonadditive set functions) is built and applied to the investigation of convergence in the distribution of random closed sets in terms of their capacity functionals. The final chapter returns to statistical applications, namely to coarse data analysis. The book contains many exercises and would provide graduate students with an excellent course before studying advanced papers on the topic.

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